Question

The molar specific heats of an ideal gas at constant pressure and constant volume are denoted by C_p and C_v respectively. If `gamma = "C"_"p"/"C"_"v"` and R is the universal gas constant, then Cp is equal to ______.

पर्याय

• `(gamma - 1)/"R"`

• `(gamma - 1)^2/"R"`

• `(gamma - 1)/(gamma"R")`

• `(gamma"R")/(gamma - 1)`

Answer 1

The molar specific heats of an ideal gas at constant pressure and constant volume are denoted by C_p and C_v respectively. If `gamma = "C"_"p"/"C"_"v"` and R is the universal gas constant, then Cp is equal to `underline((gamma"R")/(gamma - 1))`.

Explanation:

`gamma = "C"_"p"/"C"_"v"   ...."C"_"p" - "C"_"v" = "R"`

`"C"_"v"/"C"_"p" = 1/gamma`

`("C"_"v" - "C"_"p")/"C"_"p" = (1 - gamma)/gamma`

`"R"/"C"_"p" = (gamma - 1)/gamma`

`therefore "C"_"p" = (gamma"R")/(gamma - 1)`